Distributed co-operating nodes using time reversal

ABSTRACT

Dynamic, untethered array nodes are frequency, phase, and time aligned, and used to focus their transmissions of the same data coherently on a target, using time reversal. Alignment may be achieved separately for the radio frequency (RF) carriers and the data envelopes. Carrier alignment may be by phase conjugation. The data is distributed across the nodes. Data distribution and/or alignment may be performed by a Master node of the array. The nodes capture a sounding signal from the target, in the same time window. Each node converts the captured sounding signal to baseband, for example, using in-phase/quadrature downconversion. Each node stores the baseband samples of the sounding pulse. Each node convolves time-reversed samples of the sounding signal with the data, and upconverts the convolved data to radio frequency. The nodes emit their respective convolved and upconverted data so that the emissions focus coherently at the target.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority from U.S. Provisional patentapplication Ser. No. 14/247,229, entitled DISTRIBUTED CO-OPERATING NODESUSING TIME REVERSAL, filed on 7 Apr. 2013, now allowed; which claimspriority from (1) U.S. Provisional Patent Application Ser. No.61/829,208, entitled APPARATUS, METHODS, AND ARTICLES OF MANUFACTURE FORCOLLABORATIVE BEAMFOCUSING OF RADIO FREQUENCY EMISSIONS, filed on 30 May2013; and from (2) U.S. Provisional Patent Application Ser. No.61/809,370, entitled APPARATUS, METHODS, AND ARTICLES OF MANUFACTURE FORCOLLABORATIVE BEAMFOCUSING OF RADIO FREQUENCY EMISSIONS, filed on 7 Apr.2013. Each of the above-identified patent documents is herebyincorporated by reference in its entirety as if fully set forth herein,including text, figures, claims, tables, computer program listingappendices, and all other matter (if present).

The present patent application is related to the followingcommonly-owned patent documents: U.S. Provisional Patent ApplicationSer. No. 61/481,720, entitled DISTRIBUTED CO-OPERATING NODES USING TIMEREVERSAL FOR COMMUNICATIONS, SENSING & IMAGING, filed on 2 May 2011;U.S. Provisional Patent Application Ser. No. 61/540,307, entitledDISTRIBUTED CO-OPERATING NODES USING TIME REVERSAL FOR COMMUNICATIONS,SENSING & IMAGING, filed on 28 Sep. 2011; and U.S. Provisional PatentApplication Ser. No. 61/881,393, entitled APPARATUS, METHODS, ANDARTICLES OF MANUFACTURE FOR COLLABORATIVE ARRAY COMMUNICATIONS INCLUDINGBEAMFOCUSING OF EMISSIONS, filed on 23 Sep. 2013. Each of these patentdocuments is hereby incorporated by reference in its entirety as iffully set forth herein, including text, figures, claims, tables, andcomputer program listing appendices (if present).

FIELD OF THE INVENTION

This document relates generally to radio frequency (RF) communicationsand clock synchronization of untethered nodes.

BACKGROUND

The use of multiple transmit/receive antennas in wireless networkspromises mitigation of interference and high spectral efficienciesthrough concentrating signals along a designated direction ortransmission path. Compared to single-antenna-to-single-antennatransmissions, transmit beamforming may yield increased range (e.g., anN-fold increase for free space propagation), increased rate (e.g., anN²-fold increase in a power-limited regime), increased power efficiency(e.g., an N-fold decrease in the net transmitted power for a fixedreceived power), and/or may allow splitting a high data-rate stream intomultiple lower data-rate streams. (Here, N is the number of cooperativenodes or antenna elements at the transmit side.)

Distributed coherent RF transmit beamforming is a form of cooperativecommunication in which two or more information sources simultaneouslytransmit a common message, controlling the phase and delay of theirtransmissions so that the signals constructively combine at an intendeddestination. The term “beamforming” may also be used to indicate what ismore commonly referred to as directional beamforming. In this case theinformation sources are configured to produce a beam that isapproximately collimated in a given direction and the beam is notspecifically focused to maximize power at any one location, but only inone direction. Phased arrays where the locations of the individualelements and the target receiver are known, where the array elements areinterconnected with cables or other calibrated interconnections, andwhere a common centralized clock/time reference can be distributed amongthe array elements, can be configured to operate in such directionalbeamforming mode.

However, decentralized arrays, where the nodes are independentuntethered devices with independent clocks i.e., without distributedclock or frequency reference, and where the positional coordinates areunknown, are much more difficult to use as coherent phased arrays,either in transmit mode or receive mode. For such systems of devices tooperate as phased arrays, they should perform two major tasks.

First, as with any phased array, they must acquire the correct channelinformation between the array members and the intended target/source andprovide a mechanism for the nodes to transmit/receive a correctlyweighted signal at each of the array elements so that beamforming isachieved to within an accuracy required by the system.

Second, the array should implement a distributed algorithm across themembers of the array that enables the array to operate in a coherentmanner, providing phase, frequency, and time alignment of the clocks andoscillators of the different array members of the array. A correctmethod of producing this coordination of the array members is essentialto the correct operation of the phased array.

Since multiple clocks are used across the array, the algorithm shouldoperate fast enough to provide the required alignment within time limitsdetermined by the clock coherence.

Even with atomic clocks, the clock coherence limit is eventuallyreached. In a phased array, exceeding the coherence limit may manifestas a random scrambling of the phases of the carrier waves utilized inthe beamforming and hence a failure to achieve optimal or even minimallyacceptable performance.

To correct for this, the algorithm should be compatible with therequirement that the system alignment be periodically refreshed tocompensate for limited clock coherence and for operation of the array indynamic and changing channels.

Another desirable characteristic is that the algorithm be capable ofaligning the system (array members/elements/nodes) in a manner thatminimizes the required information sharing and other communicationbetween the array members.

In what follows, we will describe the arrays in transmit mode, forsimplicity. But the ideas are easily applied to receive mode operations.

In general, existing implementations fall into three broad categories.First there are those categories where the array transmitters arerequired to determine or calculate the correct beamforming weights tofocus at a known target and where the location of the transmitters andtarget is known. This is the most common type of phased arrayimplementation and is often referred to as an “open-loop” array. Suchimplementation clearly requires time, frequency, and phasesynchronization across the array. Because the various nodes may sendsignals at different times with different phase offsets, they should allagree on a common time base and a method for ensuring that the signalsarrive at the target with their carriers at the same frequency and inperfect phase alignment to avoid fading. FIG. 7 illustrates selectedelements of Open Loop Basic Array, wherein N untethered, randomlydistributed array elements are configured to operate as a basic phasedarray to produce beamforming to a target location determined by thearray itself. The formula in the Figure, s(t)=Σ_(i=1)^(N)a_(i)(t−(τ_(i)+T))cos(ω(t−(τ_(i)+T))), means that the signal at thetarget is a summation of the signals produced at the target by theelements i of the array, each with a time-dependent envelope a_(i),delayed by the corresponding time of flight (τ_(i)+T). The array doesnot require communication (information flow as such) from the targetlocation. It simply calculates the required delay offsets to ensure thatthe signals from each element are aligned at the target (some designatedbeamfocus point). The location of the target may be defined with respectto a reference point on the array, or elsewhere. When the locations ofthe array elements are fully known and the clocks of the elements aresynchronized, it is relatively simple to operate such an array. If theclocks are not synchronized, and/or if the element locations areunknown, however, such arrays are not well suited for beamfocusing,because it is difficult or impossible to calculate how far the elementsare from the focus point (the target), nor can it be accuratelyspecified when each element should launch its signal. This arrayconfiguration would typically be used for LoS targets, since, bydefinition, the array has no information regarding the channel impulseresponse other than the simple straight line distance to the target. Tofocus in NLoS environments generally requires detailed knowledge of thechannel impulse response of the NLoS channel. If this channelinformation could be made available for each node element through someother means (e.g., information flow from the target to the individualarray elements), then it would be possible to focus to a NLoSenvironment. But this is not defined as part of the array configurationproperties.

A second general category of array architectures is the “retrodirectivearray,” described with reference to FIG. 8 and FIG. 9. The formula inFIG. 8 is the same one as in FIG. 7 (s(t)=Σ_(i=1)^(N)a_(i)(t−(τ_(i)+T))cos(ω(t−(τ_(i)+T)))), and has the same meaning. Inthis array configuration, the array is assumed to be untethered andrandomly distributed. The basic principle of the retrodirective array isthat the signal acquisition phase (i.e., sounding process) enables thearray to measure and calculate a set of relative delays τ_(i) of thesignal coming from the target and arriving at each node. ConventionalState of the art arrays attempt to measure the delays of the arrivingsignals and to send a signal in return where each array element isadjusted in time to compensate for this delay so that all the signalsreturn to the target node at the same time. Proper design may enable aretrodirective array to operate with the full array gain. Retrodirectivearrays generally can operate in NLoS channels (as well as in LoSchannels), since the array elements have the information about the NLoSchannel from the sounding process and channel reciprocity. The knowledgeof the X,Y,Z coordinates of the array elements is not required forproper operation of the main channel between the cooperative array andthe target. Accurate clock synchronization, however, is needed.

This type of array is not strictly open loop, since it requires asounding pulse or an opportunistic signal detected from the target. Itis also not a closed loop system in the conventional sense, since thereis no transmission of information or messages back and forth between thearray and the target for control and alignment purposes (see concept ofcooperative arrays below). In a closed-loop system, the target receiverdetermines what alignment is required by the transmitter nodes and sendsthat information back to the transmitters. In the system describedabove, the transmitter array determines the correct procedure and neednot receive feedback from the target receiver informing it how wellaligned the system (the array) is.

In principle, all control of the operation of the array may be performedat the array end, and the sounding pulse is simply a way to acquirechannel information. This type of array may be very important in dynamicarray configurations in noisy environments. Because the array operationdoes not require information transmission across the channel foralignment purposes, it may be less susceptible to jamming andinterference. The process of clock synchronization of independent anduntethered clocks, however, does require transmission of informationback and forth between the array elements, and may present a challengeand be susceptible to interference.

In a third category of array architectures, the target receiver iscapable of communicating with each transmit array node, and the targetcan determine when optimal beamforming has been achieved. In such arrayconfigurations, the array is assumed to be untethered and randomlydistributed (ad hoc). The target is assumed to be a cooperative node andbe capable of sending information to the array. The array operation canbe controlled, for example, from the target or from the array itself,but the assumption is that a full closed loop operation is used thatenables effective alignment, when both ends of the channel are capableof communicating information relevant to the beamfocusing operation. Itis usually assumed that the target has the ability to determine whenoptimal beamforming has been achieved. For example the target may beable to assess the power density of the focused spot, or it may be ableto measure BER in a communication system. It may also be required todetermine from this signal how to adjust the required parameters of thearray to optimize or improve the beamforming and to be able tocommunicate appropriate signals to the array to achieve this goal. It isthe responsibility of the target to return control signals to thetransmitters instructing them to modify their beamforming weights untilthe target determines that optimal beamforming has been achieved.Systems like these are often referred to as “closed-loop” systems. Inthis approach, neither the transmitters nor the receiver may haveperfect channel state information, but there is a low-rate feedback linkfrom the receiver to the transmitters. In various applications thisarrangement may not require time or phase synchronization across themembers of the array because the receive node is assumed to be capableof instructing the transmitters to adjust their parameters to achieve anoptimal alignment.

Time synchronization across the array elements might make theperformance of such arrays much faster and simpler, but it is notrequired, because the target may attempt to determine the clockproperties of each array element and send its delay correctioninformation in a manner that takes into account the clock properties ofeach array member. The target may be responsible for handling thesynchronization of the array, since it is uniquely positioned todetermine the array performance and how the performance responds tochanges at the array end of the channel.

This type of array configuration typically demands a large alignmentoverhead and may have problems rapidly adapting to motion or changes inthe channel properties. It may also be susceptible to jamming andinterference, since it requires a low error rate communication channelto be available between opposite ends of the channel between the targetand the array.

Irrespective of the particular category described above, the resultantbeam shape at the receiver may resemble a phased-array radiationpattern, with one main lobe and multiple undesired side lobes that causeinterference. In conventional phased-array systems, it may also bedifficult or impossible to support coherent addition of wave-fronts inmultipath (MP) environments, and most beamforming approaches assumeline-of-sight (LoS) links between transmitters and receiver.

The problem of array alignment becomes rather difficult when theindividual member of the transmitter array are free to move with respectto each other, and do not share a common local oscillator (LO)reference, because the phases/frequencies may vary from one array memberto another, and because the timing of transmission may change as theelements move with respect to each other and with respect to thereceiver, as is typical in dynamic environments. The movements andchanges in the channel may seriously degrade the alignment required forreliable collaborative communications in an ad hoc array system.

Needs exist in the art for improved communication techniques fordistributed coherent communications, and for apparatus, methods, andarticles of manufacture enabling such improved communications. Needsexist in the art for phase/frequency synchronization techniques that canbe used in ad hoc nodes of a distributed transmitter array for coherenttransmissions.

SUMMARY

Embodiments, variants, and examples described in this document aredirected to methods, apparatus, and articles of manufacture that maysatisfy one or more of the above described and/or other needs.

In an embodiment, a method of configuring a plurality of radio frequencytransmission nodes into a distributed time reversal mirror fortransmitting to a target includes: (1) step for phase alignment of localclock references of all nodes of the plurality of radio frequencytransmission nodes; and (2) step for frequency alignment of the localclock references of all nodes of the plurality of radio frequencytransmission nodes.

In an embodiment, a method of configuring a plurality of radio frequencytransmission nodes into a distributed time reversal mirror fortransmitting to a target includes aligning phases of local clockreferences of all nodes of the plurality of radio frequency transmissionnodes. The method also includes aligning frequencies of the local clockreferences of all nodes of the plurality of radio frequency transmissionnodes. The method additionally includes aligning time references of allnodes of the plurality of radio frequency transmission nodes. The methodfurther includes distributing common data for transmission to the targetacross the plurality of nodes. The method further includes receiving, ateach node of the plurality of nodes, a sounding signal from the targetwithin a common time capture window. The method further includesgenerating, at said each node, a time-reversed sounding signal atcarrier frequency, the time-reversed sounding signal of said each nodebeing generated by sample-reversal of the common time capture window atbaseband and phase-conjugation at carrier frequency. The method furtherincludes convolving, at said each node, the common data with thetime-reversed sounding signal, thereby obtaining a transmission signalof said each node. The method further includes transmitting, from saideach node, said transmission signal of said each node, wherein the stepof transmitting is performed at the same time from all the nodes of theplurality of nodes for coherent time-reverse focusing on the target intime and space. In aspects, I/Q processing is used.

In an embodiment, the plurality of nodes includes a master node and atleast two slave nodes, and the method further includes configuring theat least two slave nodes to focus time-reversed master soundingemissions on the master node in time and space, and attempting tooptimize reception of the emissions at the master node. The steps ofconfiguring and attempting are performed before the step oftransmitting.

In an embodiment, a node includes an antenna, a radio frequencytransceiver coupled to the antenna, a local oscillator, and a processorcoupled to the transceiver to control operation of the transceiver. Thenode is part of a plurality of nodes. The node includes a means forphase alignment of the local oscillator with the local oscillators ofother nodes of the plurality of nodes. The node also includes a meansfor frequency alignment of the local oscillator with of the localoscillators of the other nodes of the plurality of nodes. In aspects,the node is configured to: (1) obtain common data for transmission fromthe plurality of nodes to a target; (2) receive a sounding signal fromthe target within a time capture window common to the plurality ofnodes; (3) generate a time-reversed sounding signal at carrier frequencyusing sample-reversal of the time capture window at baseband andphase-conjugation at carrier frequency; (4) convolve the common datawith the time-reversed sounding signal, thereby obtaining a transmissionsignal; and (5) transmit the transmission signal, wherein all the nodesof the plurality of nodes transmit simultaneously for coherenttime-reverse focusing of transmissions carrying the common data on thetarget in time and space. In aspects, the node is configured to generatethe time-reversed sounding signal and to convolve the common data usingI/Q processing.

In an embodiment, an article of manufacture has machine-readable storagemedium with program code stored in the medium in a non-volatile manner.When the program code is executed by at least one processor of a radiofrequency communication node that has an antenna, a radio frequencytransceiver coupled to the antenna, a local oscillator, and a processorcoupled to the transceiver to control operation of the transceiver, itconfigures the node to perform a number of tasks. The node is part of aplurality of nodes. The tasks include phase alignment of local clockreferences of all nodes of the plurality of radio frequency transmissionnodes, frequency alignment of the local clock references of all nodes ofthe plurality of radio frequency transmission nodes, and time alignmentof the nodes. The tasks may further include obtaining common data fortransmission from the plurality of nodes to a target; receiving asounding signal from the target within a time capture window common tothe plurality of nodes; generating a time-reversed sounding signal atcarrier frequency, the time-reversed sounding signal being generated bysample-reversal of the time capture window at baseband andphase-conjugation at carrier frequency; convolving the common data withthe time-reversed sounding signal, thereby obtaining a transmissionsignal; and transmitting said transmission signal, wherein the step oftransmitting is performed at the same time from all the nodes of theplurality of nodes for coherent focusing on the target in time andspace.

These and other features and aspects of the present invention will bebetter understood with reference to the following description, drawings,and appended claims.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 illustrates selected components of a communication arrangement;

FIG. 2 illustrates selected elements of a communication apparatusconfigured in accordance with one or more features described in thisdocument;

FIG. 3 illustrates distributed beamforming;

FIG. 4 illustrates selected aspects of modulation alignment andmisalignment;

FIG. 5 illustrates selected aspects of carrier alignment andmisalignment;

FIG. 6 illustrates selected aspects of the effects of frequencymisalignment;

FIG. 7 illustrates selected elements of an open loop basic array;

FIGS. 8 and 9 illustrate retrodirective array operation;

FIG. 10 is a summary diagram of certain attributes of the open looparrays, retrodirective arrays, and cooperative arrays;

FIG. 11 shows graphs of alignment latency as a function of the meandistances scale for selected arrays;

FIG. 12 illustrates selected aspects of operations usingupconversion-downconversion architectures;

FIG. 13 illustrates selected aspects of time-reversal transform andretransmission; and

FIG. 14 illustrates selected steps of a process for communication froman array of nodes to a target.

DETAILED DESCRIPTION

In this document, the words “embodiment,” “variant,” “example,” andsimilar words and expressions refer to a particular apparatus, process,or article of manufacture, and not necessarily to the same apparatus,process, or article of manufacture. Thus, “one embodiment” (or a similarexpression) used in one place or context may refer to a particularapparatus, process, or article of manufacture; the same or a similarexpression in a different place or context may refer to a differentapparatus, process, or article of manufacture. The expression“alternative embodiment” and similar words and expressions are used toindicate one of a number of different possible embodiments, variants, orexamples. The number of possible embodiments, variants, or examples isnot necessarily limited to two or any other quantity. Characterizationof an item as “exemplary” means that the item is used as an example.Such characterization does not necessarily mean that the embodiment,variant, or example is preferred; the embodiment, variant, or examplemay but need not be a currently preferred embodiment, variant, orexample. All embodiments, variants, and examples are described forillustration purposes and are not necessarily strictly limiting.

The words “couple,” “connect,” and similar expressions with theirinflectional morphemes do not necessarily import an immediate or directconnection, but include within their meaning connections through mediateelements.

References to “receiver” (“Rx”) and “transmitter” (“Tx”) are made in thecontext of examples of data transmission from the transmitter to theintended or target receiver. For time reversal communication techniques,the intended or target receiver may need to transmit to the transmittera sounding signal, e.g., a pulse/burst or a pilot signal, and thetransmitter may need to receive the sounding signal. Moreover, datacommunications can be bi-directional, with transceivers on both endnodes. In this document, the nodes of a cooperative array are“transmitters” of data, which they transmit to an “intended receiver”(or “targeted receiver,” “target Rx,” or simply “target”), such as abase station. The roles may be reversed, with the cooperative array (orany of its nodes) also or instead being the intended or targetedreceiver. In the event that the intended meaning is different, we willspecify explicitly, in context, what configuration is being assumed.

The expression “processing logic” should be understood as selected stepsand decision blocks and/or hardware for implementing the selected stepsand decision blocks. “Decision block” means a step in which a decisionis made based on some condition, and process flow may be altered basedon whether the condition is met or not.

Array “nodes,” “elements,” and “members” are used interchangeably.

Other and further explicit and implicit definitions and clarificationsof definitions may be found throughout this document.

Reference will be made in detail to several embodiments that areillustrated in the accompanying drawings. Same reference numerals may beused in the drawings and this description to refer to the same apparatuselements and method steps. The drawings are in a simplified form, not toscale, and omit apparatus elements and method steps that may be added tothe described systems and methods, while possibly including certainoptional elements and/or steps.

Various communication techniques described in this document employ timereversal (TR) to facilitate transmission and reception through physicalchannels that are not necessarily known a priori, and that maycontinually vary. Time reversal uses the reciprocity property of waveequations. Time reversal is described, for example, in the patentdocuments incorporated by reference above. Briefly, in a system thatuses time reversal, a pilot or an opportunistic sounding signal (e.g., asounding burst) is sent from the target antenna of the Rx to the Tx; theTx receives the sounding signal and captures in its analog-to-digitalconverter (ADC) the Channel Response (CR) of the channel between the Rxantenna and the Tx. The Tx may then be configured to send data back tothe Rx by convolving the data with the time-reversed version of thecaptured CR. Standard modulation techniques may be used to apply thedata to the signal by convolving a binary data stream with thetime-reversed CR (TR-CR). For example, the Tx may be configured to usethe TR-CR as its data pulse/burst. When the TR-CR is launched back downthe same channel by the Tx, the actual physical channel that created themultipath now acts as its ideal (or near ideal, as the case may be inthe real world) spatial-temporal matched filter and becomes a perfect(or near perfect) equalizer for the signal, creating a pulse at theintended receiver that captures much of the energy present in theoriginal CR. In effect, this can create significant multipath gain.Communication systems employing TR also have the flexibility to operatein 1×N, M×1, or M×N antenna configurations, with the ability to deriveadditional gain over and above the MP gain. The systems can focus asignal both spatially and temporally at a designated point in space,within the diffraction limits. They can operate with no LoS visibilityof the receiver, no knowledge of the location of the receiver, and noarray or dish antenna at the transmit end of the link. Additionally,there is no requirement to sweep or scan the Tx array, and the processdoes not require complex space-time algorithmic processing orcalculation, or implementation of a Rake filter to remove the signaldistortion created by long MP decay times.

The sounding signal may be a sharp pulse approaching an impulse, aGaussian pulse, chirp, barker code, Gold code, or another appropriateburst with substantially flat frequency response in the communicationband, and having a good autocorrelation function (i.e., approaching thatof an impulse function), as is known in communication theory and relatedfields (e.g., CDMA, autocorrelation radar).

FIG. 1 illustrates in a high level, block-diagram manner, selectedcomponents of a communication arrangement 100. This arrangement includesan array of ad hoc nodes 105 that may communicate with each other. Thenodes may communicate using peer-to-peer (node-to-node) communicationsor through a selected node such as a master node described below. Thereis no requirement that each of the nodes be capable of communicatingwith each other node, though some embodiments implement suchcommunications. The selected node, however, may communicate with eachother node. Note that the selected node designation may change in thecourse of operation, that is, a different node may become a selected ormaster node. As shown, the array 105 includes five distributedcooperating nodes, 105-1 through 105-5. In similar arrangements, thearray 105 may include any number of a plurality of nodes 105, forexample, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more. The arrangement 100 alsoincludes a base station 110. The nodes 105 may represent transceivers ofdifferent soldiers of a squad, and the base station 110 may be atransceiver of a command center in a Humvee, tank, or another localheadquarters or control center. (The term “base station” may haveoperational significance in some implementations, but in this documentits technical meaning is the same as the meaning of “target receiver”defined above; it may simply be a communication system to which thearray intends to direct its communications.)

The nodes 105 may be within Line-of-Sight (LoS) of each other and cancommunicate directly with each other via array links 120. Although links120-1, 120-2, 120-4, and 120-5 are shown as connecting the node 105-3 toeach of the remaining node 105, this is an exemplary arrangement; moregenerally, any of the nodes 105 may be connected by such array link 120to any of the other nodes 105. The array links 120 may be implemented,for example, using short-range RF link such as a Bluetooth® link, WiFi,or other short-, medium-, and longer-range technologies. Thetechnologies of the array links 120 may be standardized or proprietary.

The nodes 105 may be ad hoc, meaning that (1) they are free to move androtate not only relative to the base station 110 and/or the environment,but also relative to each other; and (2) they are not hardwired and donot share a common physical LO. The distances between any two of thenodes 105 are typically much smaller (by a factor of 10, 100, 1000, oranother large number, for example) than the distance between any of thenodes 105 and the base station 110. Additionally, the nodes 105 are nottethered to each other, in the sense that each of the nodes may operateusing its own physical time reference or LO, and the antennas of thedifferent nodes 1-5 are not electrically/physically connected to eachother. Each of the nodes 105 may have a single antenna, or multipleantennas.

FIG. 2 illustrates selected elements of an apparatus 200 configured inaccordance with one or more features described in this document. Theapparatus may be any of the cooperative transceivers 105 and/or the basestation 110. The apparatus may include a processor 205; a storage device210 (which may store program code for execution by the processor 205); areceiver 215 configured to receive radio frequency transmissions(including scattered/MP transmissions) from one or more othertransceivers/base stations; a transmitter 220 configured to transmitradio frequency transmissions to the other transceivers/base stations;and one or more transmit and receive antennas 225 coupled to thereceiver 215 and the transmitter 220. A bus 230 couples the processor205 to the storage device 210, the receiver 215, and the transmitter220; and allows the processor 205 to read from and write to thesedevices, and otherwise to control operation of these devices.

The nodes 105 are configured to communicate coherently (in asynchronized manner) with the base station 110. The communication is“coherent” in the sense that the nodes 105 can transmit the same data tothe base station 110 in a synchronized manner so that the radiofrequency transmissions from all or a plurality of the nodes 105 addcoherently in time and space at the receiving antenna(s) of the basestation 110. Note that the concept of “synchronization” does notnecessarily require explicit knowledge by the nodes of their relativephases (but may include such explicit knowledge); it does mean knowledgesufficient to launch the emissions from the nodes so that the emissionsfocus in time/space (combine constructively) on the target receiver.

We next discuss certain considerations for designing distributedbeamforming systems using up/down conversion transceivers.

FIG. 3 illustrates antennas TX1 and TX2 of two distributed nodes (suchas the nodes 105 of FIG. 1). The antennas TX1 and TX2 transmit to anantenna RX of the target receiver (such as the base station 110). Thetransmitted waveforms have shared data (“1 0 1” in the example shown inthe Figure). The transmit times and the paths from the node antennas TX1and TX2 to the target receiver antenna RX are such that thetransmissions add coherently in time and space at the target receiverantenna RX. By adding coherently, we mean that the symbol/modulationenvelopes and the underlying carriers of the separate TX1 and TX2signals emitted from the respective TX1/TX2 antennas arrivesimultaneously at the targeted receiver antenna RX (before receivecircuitry). When both the symbol (envelope) alignment and carrieralignment perfectly overlap at the RX, the distributed array may achieveperfect or near perfect array gain at the intended receiver antenna RX,as is shown in FIG. 3. If these conditions are not met, the emittedsignals from TX1 and TX2 will not arrive coherently at the RX and arraygain will not be achieved (including the possibility of destructiveinterference with its attendant signal attenuation relative to receptionof a single transmitter signal).

The use of TR at the transmit array nodes may solve this alignmentproblem. In certain implementations of this technology the transmitnodes capture the entire sounding signal, e.g., the pulse envelope andunderlying carrier frequency, and time reverse both of these components.This requires that digital storage mechanisms in the analog-to-digital(A/D) converter chain in the transceivers located at the transmit nodesare capable of capturing the entire carrier frequency. For example, ifthe sounding pulse is a one microsecond wide Gaussian pulse on a 60 GHzcarrier, minimal digital resources may be needed to capture the pulseenvelope, but it may far exceed the capability of most commercial A/Dconverters to capture the 60 GHz carrier. Consequently, the systems ofinterest typically downconvert the incoming signal to a much lowerfrequency (the intermediate frequency or simply IF) or to baseband(substantially zero frequency) before capturing it in the digitalsampling infrastructure. It is the downconverted component that is thensubsequently time-reversed. This lower bandwidth time-reversed channelresponse (TR-CR) is then upconverted back to the correct carrierfrequency before retransmission to the target. However, the use of LocalOscillators (LOs) at the nodes to produce the upconversion anddownconversion creates a level of complexity in the array time-reversalprocess that requires additional alignment and imposes synchronizationrequirements between the nodes that are not required in the simpler TRprocess. The array beamforming process may address beamforming throughalignment of (1) the carrier, and (2) the lower bandwidth modulationenvelopes, separately.

Below, we address the specific implementations of TR arrays that operatein heterodyne or homodyne mode using upconversion and downconversionwith LOs, and compare how the system may operate with or without theconventional in-phase and quadrature (I/Q detection techniques that arestandard for many communication applications. As may be appreciated by aperson skilled in the art after perusing this document and the attachedFigures, although I/Q detection is used in the industry, its use in adhoc arrays is not a straightforward matter.

The underlying assumption of TR communications is that the target isable to emit a sounding signal which can be detected by each arrayelement. (It may of course happen that some array elements do not detectit, for whatever reason; the remaining elements may then be consideredas the “array.”) There is no assumption that the array and the targetare cooperative, hence the “sounding pulse” may actually be anopportunistic signal (of whatever shape) acquired by the array. Incooperative applications (where the target and the array cooperate), thesignal may be a pilot data sequence or other specially tailored pulse orother format. Whatever the nature of the target's transmission, we mayrefer to it here as a sounding “pulse,” although it should be understoodthat the actual signal need not be a single pulse. How the pulse isprocessed generally depends on the intended application of the array. Incommunications applications, for example, it may be necessary for eacharray element to deconvolve the channel impulse response from theacquired sounding signal. In power focusing applications, this may notbe necessary.

In operation, the array receives a sounding signal emitted from thetarget. We denote the sounding signal by q(t)=A(t)cos(ω₁t+ψ), with thetotal pulse duration T₀ and carrier frequency ω₁. We arbitrarily definethe reference time t=0 at the target. Since one LO is used at the targetand a different LO at each array node, a phase offset difference betweenthe different nodes (as well as between each of the array nodes and thetarget) must be allowed for, even if identical frequencies are somehowguaranteed, unless there is another means for synchronizing the phases.Without loss of generality, let us assume the phase ψ=0. If the LO atthe target is designated by p_(Rx) (t)=cos(ω₁t), the LO at a node of thetransmit array may be designated by p_(TX)(t)=cos(ω₀t+φ_(c)).

We now pass the signal q(t) through a multipath channel and obtain atthe jth transmit array node TX_(j)

${s_{j}(t)} = {\sum\limits_{i = 1}^{n}\;{\alpha_{i,j}{A\left( {t - \tau_{i,j}} \right)}{{\cos\left( {\omega_{1}\left( {t - \tau_{i,j}} \right)} \right)}.}}}$

To simplify notation, for now, let us examine the expression for asingle Tx antenna, which permits us to drop the j index temporarily. Wecan re-write the previous formula:

${s(t)} = {\sum\limits_{i = 1}^{n}\;{\alpha_{i}{A\left( {t - \tau_{i}} \right)}{{\cos\left( {\omega_{1}\left( {t - \tau_{i}} \right)} \right)}.}}}$

It can be written in IQ format as

${s(t)} = {{\sum\limits_{i = 1}^{n}\;{\left\lbrack {\alpha_{i}{A\left( {t - \tau_{i}} \right)}{\cos\left( {\omega_{1}\tau_{i}} \right)}} \right\rbrack{\cos\left( {\omega_{1}t} \right)}}} + {\sum\limits_{i = 1}^{n}\;{\left\lbrack {\alpha_{i}{A\left( {t - \tau_{i}} \right)}{\sin\left( {\omega_{1}\tau_{i}} \right)}} \right\rbrack{{\sin\left( {\omega_{1}t} \right)}.}}}}$which is equivalent tos(t)=I(t)cos(ω₁ t)+Q(t)sin(ω₁ t).where

${I(t)} = {\sum\limits_{i = 1}^{n}\;\left\lbrack {\alpha_{i}{A\left( {t - \tau_{i}} \right)}{\cos\left( {\omega_{1}\tau_{i}} \right)}} \right\rbrack}$${Q(t)} = {\sum\limits_{i = 1}^{n}\;{\left\lbrack {\alpha_{i}{A\left( {t - \tau_{i}} \right)}{\sin\left( {\omega_{1}\tau_{i}} \right)}} \right\rbrack.}}$

Standard IQ processing allows recovery of I(t) and Q(t) by firstsplitting the signal s(t) into two copies, multiplying each copy byquadrature Local Oscillator signals cos (ω₀t+φ_(c)) and sin (ω₀t+φ_(s)),and capturing each result of the multiplication separately in a samplingdevice with a sampling frequency at least 2× the highest frequencycomponent in the signal. This is the downconversion process referred toabove. In practice, φ_(c) and φ_(s) can be made equal, even if theycannot be eliminated but we will handle them separately at this stage topreserve generality. In general, each Tx node will have a differentvalue of φ_(c) and φ_(s), and it may be shown that it is precisely thesedifferent values that may be aligned as part of the array alignmentprocess. Two distinct signals result from the downconversion:s _(c)(t)=0.5(I(t)cos [(ω₁−ω₀)t−φ _(c) ]+Q(t)sin [(ω₁−ω₀)t−φ _(c)])s _(s)(t)=0.5(Q(t)cos [(ω₁−ω₀)t−φ _(s) ]−I(t)sin [(ω₁−ω₀)t−φc]).

This result assumes that any terms with (ω₁+ω₀) can be substantiallyremoved by filtering. In general, the (ω₁−ω₀) terms are intermediatefrequency terms, which can be captured in the sampling device, and maybe useful for additional processing. The special case where ω₁=ω₀represents downconversion to baseband. In general, when (ω₁−ω₀)=0 werefer to the system as a homodyne system, and when (ω₁−ω₀)≠0 we refer tothe system as a heterodyne system. When these terms are used we normallyassume that the frequency difference in a heterodyne system is adeterminsitic and significant frequency. Other issues may arise when(ω₁−ω₀)≈0, i.e., in a nominally homodyne system with unintended smallfrequency offsets due to errors.

Because of the multipath, it may not be possible to remove the terms cos(ω₁τ_(i)) and sin (ω₁τ_(i)) by squaring and adding, due to the manycross-terms that arise when the summation terms are squared. Hence,these terms are fading terms which will vary randomly depending on themultipath details. It is the presence of significant multipath that mayprevent conventional I/Q from operating correctly.

Time Reversal

At this stage, two separate signals s_(c)(t) and s_(s)(t) have beencaptured. Their frequencies are low enough to allow their capture anddigitization to be performed in an A/D converter. The signals are thentime-reversed. Time reversal of a signal means that the direction of thesignal is reversed by applying the transformation t→−t. To do thisproperly, however, the correct delay should be carefully applied to theoutgoing signal.

Consider the following explanation. A pulse φ(t) is defined at somepoint t=0 and transported to a location where it arrives at some timeτ_(i) later. We denote the “transport” function by φ(t′)=φ(t−τ_(i)). Ifwe reverse the pulse and define the pulse by φ′(t)=φ(−t) and transportit to the same location, we now describe the pulse by φ′(t′)=φ(τ_(i)−t).

When this is applied to a sequence of multipath delayed pulses as shownin FIG. 13, in the simplest implementation everything is captured in atime frame ranging from t=0 to t=T where T is long enough to capture allor practically all the multipath echoes. The principle of the techniqueis that in TR this signal is read out of the sampler (storage buffer)starting at time t=T as is illustrated (or at a later time T+t_(inc)),and the read-out of the signal proceeds in reverse (last in, first out),continuing till time t=2T (if the read out started at T; otherwise, tillt=2T+t_(inc)), i.e., the whole frame is read out in reverse as soon as aframe of length T is acquired (or after a delay t_(int); in thefollowing discussion, we assume t_(inc)=0). As will be seen below, whenthis process is applied across an entire array of Tx nodes of an array,it essentially implements the same process for each node as describedabove for a single node, but the time T is identical for each node,implying the need for time synchronization across the array.

After time-reversal, the I/Q terms can now be written as follows:

${I^{TR}(t)} = {\sum\limits_{i = 1}^{n}\;\left\lbrack {\alpha_{i}{A\left( {\left( {{2T} - \tau_{i}} \right) + {m\;\Delta\; t} - t} \right)}{\cos\left( {\omega_{1}\tau_{i}} \right)}} \right\rbrack}$${{Q^{TR}(t)} = {\sum\limits_{i = 1}^{n}\;{\left\lbrack {\alpha_{i}{A\left( {\left( {{2T} - \tau_{i}} \right) + {m\;\Delta\; t} - t} \right)}{\sin\left( {\omega_{1}\tau_{i}} \right)}} \right\rbrack.}}}\;$

Before setting forth the formula for the entire signal returning to thetarget, it should be recognized that if the system is used for datatransmission there may be multiple data bits transmitted at differenttimes. Hence in practice we need to convert t→2T+mΔt−t, where mΔtdenotes the delay of the mth bit, m=0 denotes the first pulse/bit, andΔt denotes the data pulse/bit period. Hence, cos [(ω₁−ω₀)t−φ_(c)]→cos[(ω₁−ω₀)(2T+mΔt−t)−φ_(c)].

Thus we have time reversed signals:s _(c,m) ^(TR)(t)=0.5(I ^(TR)(t)cos [(ω₁−ω₀)(2T+mΔt−t)−φ_(c) ]+Q^(TR)(t)sin [(ω₁−ω₀)(2T+mΔt−t)−φ_(c)])s _(s,m) ^(TR)(t)=0.5(Q ^(TR)(t)cos [(ω₁−ω₀)(2T+mΔt−t)−φ_(s) ]+I^(TR)(t)sin [(ω₁−ω₀)(2T+mΔt−t)−φ_(s)]).

These signals may be kept separate at the Tx node of the array. However,in order to transmit the signals back to the RX target, first IQ isupconverted by multiplying each signal by the LO of frequency ω₀ (or adifferent carrier frequency) and difference the terms, giving aresultant signal:s _(m)′(t)=s _(c,m) ^(TR)(t)cos(ω₀ t+φ _(c)′)−s _(s,m)^(TR)(t)sin(ω_(t)+φ_(s)′).

Note that for generality we denote the phase offset of the outgoing LOas φ′ rather than φ because we may wish to change the phase of the LOapplied to the outgoing signal compared to the LO phase applied to theincoming signal. For example, in embodiments the outgoing phase is aconjugated version of the input phase. This means that the followingsignal may be launched:

${{s_{m}^{\prime}(t)} = {0.5\begin{pmatrix}\begin{matrix}{\sum\limits_{i = 1}^{n}\;{\left\lbrack {\alpha_{i}{A\left( {\left( {{2T} + {m\;{\Delta t}} - \tau_{i}} \right) - t} \right)}{\cos\left( {\omega_{1}\tau_{i}} \right)}} \right\rbrack{\cos\left( {{\omega_{1}\left( {{2T} + {m\;\Delta\; t} - t} \right)} -}\; \right.}}} \\{\left. {{\omega_{0}\left( {{2T} + {m\;\Delta\; t}} \right)} - \theta} \right)\; +}\end{matrix} \\\begin{matrix}{\sum\limits_{i = 1}^{n}\;{\left\lbrack {\alpha_{i}{A\left( {\left( {{2T} + {m\;\Delta\; t} - \tau_{i}} \right) - t} \right)}{\sin\left( {\omega_{1}\tau_{i}} \right)}} \right\rbrack{\sin\left( {{\omega_{1}\left( {{2T} + {m\;\Delta\; t} - t} \right)} -} \right.}}} \\\left. {{\omega_{0}\left( {{2T} + {m\;\Delta\; t}} \right)} - \theta} \right)\end{matrix}\end{pmatrix}}},$where θ=φ_(c)+φ′_(c)=φ_(s)+φ_(s)′. To propagate a time-reversed signalback to the target, a transformation t→t−τ_(i) ^(R) is applied. At thepeak of the TR signal, all the delays are equalized, i.e., τ_(i)^(R)−τ_(i)=0 for all values I (perfect reciprocity). In practice, ifreciprocity is not perfectly maintained this term may not equal zero andmay create noise and fading effects. The full expression for the signalarriving at the RX target is shown below, with simplifying assumptionthat only the components that come up along path i and return along pathi are aligned (i.e., ignoring the components that come up path i andreturn on a different path j):

${p(t)} = {0.5{A\left( {{2T} + {m\;\Delta\; t} - t} \right)}{\sum\limits_{i = 1}^{n}\;{{\alpha_{i}\left\lbrack \begin{bmatrix}\begin{matrix}{{\cos\left( {\omega_{1}\tau_{i}} \right)}{\cos\left( {{\omega_{1}\left( {{2T} + {m\;\Delta\; t} - t + \tau_{i}} \right)} -} \right.}} \\{\left. {{\omega_{0}\left( {{2T} + {m\;\Delta\; t}} \right)} - \theta} \right) +}\end{matrix} \\\begin{matrix}{{\sin\left( {\omega_{1}\tau_{i}} \right)}{\sin\left( {{\omega_{1}\left( {{2T} + {m\;\Delta\; t} - t + \tau_{i}} \right)} -} \right.}} \\\left. {{\omega_{0}\left( {{2T} + {m\;\Delta\; t}} \right)} - \theta} \right)\end{matrix}\end{bmatrix} \right\rbrack}.}}}$Restating this result, we obtain:

${{p(t)} = {0.5{{A\left( {{2T} + {m\;\Delta\; t} - t} \right)}\left\lbrack {\cos\left( {{\omega_{1}\left( {t - \left( {{2T} + {m\;\Delta\; t}} \right)} \right)} + {\omega_{0}\left( {{2T} + {m\;{\Delta t}}} \right)} + \theta} \right)} \right\rbrack}{\sum\limits_{i = 1}^{n}\;{\alpha_{i}.}}}}\;$Restating again, we get p(t)=0.5γA(2T+mΔt−t)cos(ω₁t−(ω₁−ω₀)(2T+mΔt)+θ),where the TR process has eliminated the channel specific phase offsetω_(i)τ_(i) not only for the LoS channel from the Tx array node to the RXtarget, but also all the multipath channels incorporated in the channelmodel. Note that there is now no term left that depends on the channelpropagation delay τ. Hence, the TR process, even when reduced tobaseband, intrinsically and automatically performs phase conjugationthat eliminates the propagation phase offset of the main channel. Theonly remaining term that is channel specific is

${\gamma = {\sum\limits_{i = 1}^{n}\alpha_{i}}},$which is the channel loss/gain term with multipath gain included. Thisphase conjugation is applied simply by applying the time-reversalprocess and requires no additional phase conjugation process.

This signal may be split into two copies and combined with quadraturelocal oscillators cos(ω₁t) and sin(ω₁t), reducing the signal back tobaseband, as shown below:

$\begin{matrix}{{p_{I}(t)} = {\frac{1}{2\sqrt{2}}\gamma\;{A\begin{pmatrix}{{2T} +} \\{{m\;\Delta\; t} - t}\end{pmatrix}}{\cos\left( {{\omega_{1}t} - {\left( {\omega_{1} - \omega_{0}} \right)\left( {{2T} + {m\;\Delta\; t}} \right)} + \theta} \right)}{\cos\left( {\omega_{1}t} \right)}}} \\{= {\frac{1}{2\sqrt{2}}\gamma\;{A\left( {\left( {{2T} + {m\;\Delta\; t}} \right) - t} \right)}{\cos\left( {\theta - {\left( {\omega_{1} - \omega_{0}} \right)\left( {{2T} + {m\;\Delta\; t}} \right)}} \right)}}}\end{matrix}$ $\begin{matrix}{{p_{Q}(t)} = {\frac{1}{2\sqrt{2}}\gamma\;{A\begin{pmatrix}{{2T} +} \\{{m\;\Delta\; t} - t}\end{pmatrix}}{\cos\left( {{\omega_{1}t} - {\left( {\omega_{1} - \omega_{0}} \right)\left( {{2T} + {m\;\Delta\; t}} \right)} + \theta} \right)}{\sin\left( {\omega_{1}t} \right)}}} \\{= {{- \frac{1}{2\sqrt{2}}}\gamma\;{A\left( {\left( {{2T} + {m\;\Delta\; t}} \right) - t} \right)}{\sin\left( {\theta - {\left( {\omega_{1} - \omega_{0}} \right)\left( {{2T} + {m\;\Delta\; t}} \right)}} \right)}}}\end{matrix}$

Remembering that this still represents the signal due to a single Txnode of the array, it may be seen that there is a phase term whichproduces fading:θ−(ω₁−ω₀)(2T+mΔt).

This phase term has three components, to wit:

1. The first component is θ, which is produced by the difference of thephase of the LO at the Tx node of the array and the phase of the LO atthe RX target. Hence, fading is sensitive to a phase difference acrossthe entire channel between Tx and RX node.

2. The second component is (ω₁−ω₀)(2T), a static term which may occur ina heterodyne system and is a term that effectively represents thecontinual accumulation of phase of the IF frequency in a heterodynemode.

3. The third component is (ω₁−ω₀)(mΔt), which is a continuallyaccumulating phase as the IF frequency continues to change for everysuccessive data pulse emitted.

Under these circumstances, the RX array node may be configured to useI/Q detection to eliminate the phase fading. This would provide a signal

${P(t)} = {\sqrt{\left( {{p_{I}(t)}^{2} + {p_{Q}(t)}^{2}} \right)} = {{\frac{1}{2\sqrt{2}}\left\lbrack {\gamma\;{A\left( {\left( {{2T} + {m\;\Delta\; t}} \right) - t} \right)}} \right\rbrack}.}}$

Alternatively, if the system can operate in homodyne mode we are leftonly with the first term θ. Since this represents a phase differencebetween the LOs at different ends of the channel, the phase of the LO atthe Tx node of the array or the RX target may be adjusted until thisterm is reduced to 2πn, where n is an integer. We refer to this asdynamic channel phase alignment.

There is one additional technique that may be applied in a homodynechannel that removes the need for I/Q detection at the RX target.

If the RX target detects the signal using only a cosine LO and no I/Qdetection, the detected signal can be written asP(t)=γA((2T+mΔt)−t)cos(θ). Recall that we earlier definedθ=φ_(c)+φ′_(c). Without I/Q detection or dynamic phase alignment, thereis no simple way to remove this term. However, if we arrange theoutgoing LO to be a phase conjugated version of the incoming LO, then wehave φ_(c)=−φ′_(c)

θ=0 under all cases.

It should be understood that this phase conjugation process is anadditional phase conjugation over and above the phase conjugation thatis inherently applied by the time-reversal process. In a system thatproduces downconversion and upconversion as described above, this isperformed outside of the TR process, and so there is a component of theLO phase that is not automatically phase-conjugated by the TR processand requires to be separately phase conjugated. By separating the twoaspects requiring phase conjugation and by applying time reversal toperform the phase conjugation that removes the phase distortions fromthe propagation path, a system is implemented that allows performance ofthe phase conjugation of the Local Oscillators with a simplemanipulation of the signal that can be performed in the signalprocessing infrastructure.

We will now apply the results which we derived above for a channelbetween a single Tx node in an array and the RX target, to the entire Txarray of N distributed array members. Note that the array members/nodesmay be ad hoc nodes, as that term was previously defined.

It was disclosed above that the TR process removes any channel specificphase terms from the signal by the process of phase conjugation that isimplicit in the TR process. Hence each of the N nodes in an array cantime-reverse its captured sounding signals independently in an identicalor analogous manner. The question now becomes how to align in time thevarious signals, enabling them to overlap coherently at the RX node.

At this point we assume that the LO at each Tx array node can bedescribed by a phase term θ_(j)=φ_(cj)+φ′_(cj), a frequency ω₀, and TRreflection time T_(j). The signal gain/loss term along each path to theRX target is given by γ_(j), and this may include a multipath gain term.Hence, the signal arriving at the RX target is

${{p(t)} = {\sum\limits_{j = 1}^{N}{\gamma_{j}{A\left( {{2T_{j}} + {m\;\Delta\; t} - t} \right)}{\cos\left( {{\omega_{1}t} - {\left( {\omega_{1} - \omega_{0j}} \right)\left( {{2T_{j}} + {m\;\Delta\; t}} \right)} + \theta_{j}} \right)}}}},$which after in-phase detection has been performed produces the followingsignal:

${p_{I}(t)} = {\sum\limits_{j = 1}^{N}{\left\lbrack {\gamma_{j}{A_{j}\left( {\left( {{2T_{j}} + {m\;\Delta\; t}} \right) - t} \right)}{\cos\left( \eta_{j} \right)}} \right\rbrack.}}$

Using full I/Q detection, the signal may be written thus:

${P \propto \sqrt{\left\lbrack {\left( {\sum\limits_{j = 1}^{N}{\gamma_{j}A_{j}{\cos\left( \eta_{j} \right)}}} \right)^{2} + \left( {\sum\limits_{j = 1}^{N}{\gamma_{j}A_{j}{\sin\left( \eta_{j} \right)}}} \right)^{2}} \right\rbrack}},$where γ_(i) denotes the specific path loss factor on each channel, andη_(j)=θ_(j)−(ω₁−ω_(0j))(2T_(j)+mΔt) and A_(h)=A((2T_(j)+mΔt)−t). It maybe re-stated as

$P \propto {\sqrt{\sum\limits_{i = 1}^{N}{\sum\limits_{j = 1}^{N}{A_{i}A_{j}\gamma_{i}\gamma_{j}{\cos\left( {\eta_{i} - \eta_{j}} \right)}}}}.}$

Although the last expression may appear to be a very complex one, it hasan immediate advantage. The “fading” component of the term, namely cos(η_(i)−η_(j)), is a function of phase differences between the elementsthat are local to the phased array and do not require any knowledge orcontrol of a phase difference between the array and the target. This isan important characteristic, particularly where the target does notcommunicate with the array.

When the array is configured to implement a common time synchronizationwhere T_(j)→T, and a common frequency synchronization of the localoscillators of the array where ω_(0j)→ω₀, then the expression may bereduced to

$P \propto {A\;\Gamma{\sqrt{\sum\limits_{i = 1}^{N}{\sum\limits_{j = 1}^{N}{\cos\left( {\theta_{i} - \theta_{j}} \right)}}}.}}$

The fading term

$\sum\limits_{i = 1}^{N}{\sum\limits_{j = 1}^{N}{\cos\left( {\theta_{i} - \theta_{j}} \right)}}$can be eliminated with the implementation of phase synchronizationacross the elements of the array (θ_(i)−θ_(j)=0), achieving P∝AΓN².Configuring the array nodes in this way eliminates fading and producesN² array gain.

The analysis above defines how the array operates when the target canperform I/Q detection. This enables the alignment of the array to beseparated from any interaction with the target, and eliminates need fordynamic adjustment of the variables. Hence the target has no need toperform phase alignment to optimize the arriving signal.

A more complex situation arises when I/Q detection is not performed atthe target, but only a single phase of the LO is used fordownconversion. In this case, the signal recovered may be written aswhere

${{p_{I}(t)} = {{A\left( {\left( {{2T} + {m\;\Delta\; t}} \right) - t} \right)}{\sum\limits_{j = 1}^{N}\left\lbrack {\gamma_{j}{A\left( {\left( {{2T} + {m\;\Delta\; t}} \right) - t} \right)}{\cos\left( \eta_{j} \right)}} \right\rbrack}}},$where ηj=θj−(ω₁−ω₀)(2T+mΔt).

Without I/Q detection, a residual phase term is left, possibly resultingin fading. The residual phase term has two components. First, there isthe θ_(j) constant term. Second, there is the constantly varying term(ω₁−ω₀)(2T+mΔt), which changes with every data bit transmitted. Inembodiments, the system is configured so as to impose anothersynchronization condition operating between the target and the array,i.e., ω₁=ω₀, which eliminates the data dependent phase term. Assuminglocal phase synchronization across the array, we are still left with aterm cos(θ), because local phase synchronization does not alter therelative phase difference between the array and the target. This in factis more fully expressed as cos (θ_(array)−θ_(target))→1 and it mayrequire performance of a dynamic phase adjustment at the target (or thearray nodes) until θ_(array)=θ_(target). Hence in this simpler detectionmode, as with normal detection, failing to use I/Q detection may resultin fading and makes it desirable to configure the system for dynamicphase alignment between both ends of the communication link (that is,between the array and the target). This added complexity becomesunnecessary if the target can implement I/Q detection.

There may sometimes be circumstances where the target and the arraycannot easily communicate status information even if they can implementthe main channel communication link, preventing effective dynamic phasealignment from being performed. Another approach may be implemented toalleviate this problem. As mentioned earlier in the single channeldescription, another solution arises when phase conjugation of the LocalOscillator phase between the incoming and outgoing direction isimplemented. Assuming frequency and time synchronization between membersof the array, the residual phase term may be eliminated with phaseconjugation of the local oscillator where the phase of each LO at thearray for incoming signals can be written as cos(ω₀t+φ_(c)) andsin(ω₀t+φ_(c)), and the outgoing LO phase is cos(ω₀t−φ_(c)) andsin(ω₀t−φ_(c)). It can be seen that the phase is inverted, φ_(c)→−φ_(c).We refer to this as phase conjugation of the Local Oscillator. In thiscase, the combined phase term of the jth node is θ_(j)=φ_(cj)−φ_(cj)=0,which process now eliminates the phase fading effects. As in the singlechannel case, this can be implemented in the digital and analog signalprocessing infrastructure.

Methods for Producing Phase Conjugation of the LO.

It is trivial to produce a phase conjugated cosine or sine signal whenthe phase φ_(cj) is known: the phase may be adjusted to the correctvalue, −φ_(cj). The problem, however, is that there is no simple way todefine the phase of a free running local oscillator, because thatrequires a definition of time t=0. In embodiments, a shared time syncacross the array is implemented, resulting in an implicitly-defined timet=0. This may be the only condition under which correctly defined phaseconjugation is implemented. It is similar to how TR can create phaseconjugation of the channel propagation phase by defining T. Phaseconjugation across the array may be performed by conjugating withrespect to a shared time T. We define the reference phasecos(ω_(0j)T+φ_(c)) and thus the phase conjugation is the process ofcos(ω_(0j)T+φ_(c))→cos(θ_(0j)T−φ_(c)). Once this reference has beenestablished, the signal cos(ω_(0j)t−φ_(c)) may be defined.

In summary this allows achieving retrodirection with an array inhomodyne operation since both the baseband channel response (CR) isphase conjugated using TR, and the LOs are phase conjugated directly.This enables perfectly aligned retrodirection even when the signal ismixed to IF or baseband, and the receiver cannot perform I/Q detectionto remove residual phase offsets.

We have shown theoretically that for retrodirection both the carriersand the modulation envelopes have to be aligned correctly. Below, weillustrate, graphically and verbally, the effects of misalignment ofcarrier phase, carrier frequency, and data modulation in the followingparagraphs.

Data Modulation.

FIG. 4 illustrates some aspects of perfect modulation alignment, slightmisalignment of modulation, and severe misalignment of modulation cases.The data sent by TX1 and TX2 should arrive aligned at the RX antenna forthe RX to detect the data being sent. When the envelope and phase of thedata alone (i.e., stripped carrier) are considered, it can be seen howdata misalignment jumbles the incoming signals detected by the RX. Inthe perfect alignment case 4A on the left of the Figure, the datasymbols (envelope of the signal) align at the RX so that ideal arraygain may be achieved, assuming carrier alignment. When there is a slightmisalignment in the data as in case 4B in the middle, the data may stilloverlap somewhat, but the signal amplitude will be diminished relativeto the perfect alignment case, reducing the total achievable array gain.When there is major misalignment of a whole symbol as in case 4C on theright, the data will be misaligned at the RX, the symbols will notoverlap and add coherently. This potentially results in the wrong datastream being detected and an amplitude that approaches a singletransmitter case, or in the case of destructive interference, amplitudelower than in the single transmitter case. Symbol period misalignmentmay be caused by improper time synchronization and determination of timedelays with widely distributed arrays or highly disparate multipathdelays/decay spreads, for example. It should be noted that the Figureshows essentially amplitude modulated signals. These same considerationsapply to more complex modulation formats, e.g., QPSK or BPSK where thedata envelopes may have an underlying IF modulation frequency differentthan the carrier frequency.

Carrier Phase Alignment.

FIG. 5 illustrates some aspects of perfect alignment of carriers, slightmisalignment of carriers, and severe misalignment of carriers. Similarto data alignment, carrier alignment is required when the signals arriveat the RX antenna in order to achieve coherent gain of the signalstransmitted from TX1 and TX2. To understand the effects of carrier phasealignment, let us assume that TX1 and TX2 both have clocks thatoscillate at the same frequency, producing a continuous sinusoidal waveat the frequency. Unlike data alignment which has absolute timingrequirements for the data packet to align correctly, carrier alignmentis a narrowband process, equating to coherent addition of sine waves.Due to the continuous wave nature of the oscillators, phase isambiguous, because it can be shifted by multiples 360° (or 2π radians),without change in the observed signal. When there is perfect phasealignment of the continuous wave (CW) carrier signals, the peaks andtroughs of the sine waves will add coherently, resulting in twice theamplitude (for equal amplitude carriers). This is shown in case 5A onthe left of FIG. 5. When misalignment occurs, the offset sine waves willstill combine, but now parts of the peaks and troughs will subtract fromeach other, resulting in a phase shifted sine wave with diminishedamplitude. This is shown in case 5B in the middle of FIG. 5. At the veryextreme or complete phase misalignment (180°), the sine waves may becompletely incoherent, or faded. This is shown in case 5C on the rightof FIG. 5. With unlocked carrier phases, the addition of two sine waveswill result in CW signals at the RX that randomly span from completelycoherent to completely incoherent. Note that FIG. 5 shows signalswithout noise; with noise, complete misalignment may not be completelyflat.

Carrier phase offsets can be created due to differing intrinsic phasesof the LO and different phase lengths of the channel over which thesignal must travel. This is similar to compensating time of flightoffsets due to differing channel lengths for data symbol alignment. Letus assume the carriers of TX1 and TX2 are phase aligned. If both theirflight times to the RX target are equal, their sine waves will processthrough the equal length channel and remain in phase at the RX targetantenna. If the channel lengths differ, one sine wave will processlonger and arrive at the RX target with a relative phase offset. With achannel length that results in an odd multiple of 180° phase shifts, theRX will encounter a fade due to differing channels. We call this effectchannel phase offset. These effects are similar to local oscillatorphase offsets, but are distance- and motion-dependent, and should becompensated quickly if operation with dynamically moving transmittersand/or receivers is desired.

As can be seen, it is possible for the data envelopes to besubstantially aligned, but for the underlying carriers to be misaligned.This results in the correct data arriving at the RX target, but the datamay experience coherent fading due to the carrier misalignment. We referto this as carrier misalignment. It may also happen that the carriersare essentially in-phase, but the data envelopes are misaligned, inwhich case corrupted data will reach the RX target even though it iscorrectly phased. We may refer to this as symbol period misalignment. Itis also possible for a combination of both to occur. Even minormisalignment of the system can result in carrier misalignment.

Carrier Frequency Alignment.

While local oscillators may be quite accurate (for example, to within 10ppm for typical quartz crystal), they have slight frequency offsets fromone another. Frequency offsets result in misalignment of the carrierperiods (and, over long intervals, data). Thus, even with accurateinitial phase alignment of peak or trough, the mismatch in frequencywill result in non-coherent gains at the intended RX. As illustrated inFIG. 6, two sine waves with no frequency offset add coherently in timewhen phases are aligned. This is case 6A on the left of the Figure. Whenthere is a slight frequency offset, the waves add coherently at first,but then begin to diverge, with decreasing amplitude at RX after sometime. This is case 6B in the middle of the Figure. When there is a majorfrequency offset, or a small frequency offset for a longer time, thewaves become severely misaligned, case 6C on the right of the Figure.

If the frequencies are different, then the phases will eventually becomemisaligned. This can be corrected by “refreshing” the system, i.e.,realigning the phases. This process is generally disruptive to thesmooth operation of the system and its occurrence should be minimized.It is important to keep the frequencies aligned so that the phasealignment persists to an acceptable degree for as long as is appropriatefor a given system. The system applications determine how long areasonable phase coherence must persist before refresh occurs, andconsequently this will place a limit on how much frequency misalignmentcan be tolerated.

Capture Window.

One of the challenges with conventional phased arrays is that even whenfrequency, time, and phase synchronization has been implemented across aphased array, there still exists the problem of calculating what delaysto implement across the array to ensure that the signals arrive at thetarget in good time alignment, and this information changes as thetarget location changes.

In embodiments, the array is configured to implement a technique forusing TR across the array with an additional process that depends on thetime synchronization process, allowing automatic alignment of thesignals across the array without the large overhead.

It can be seen from FIG. 9 that according to this approach each node ofthe array captures the incoming sounding signal in a common time windowthat is shared by every node of the array. The start of the capturewindow represents the time that each node starts to record the incomingsounding signal, and the end of the capture window represents the timewhen each node may finish recording the incoming sounding signal. Thenode is not required to determine that a signal is actually present whenit starts to record, or where the signal is in the window. It simplyrecords for the period of the common capture window, which will resultin each node of the array capturing whatever signal arrives. The samesounding pulse may arrive at different times at various nodes due to thefact that the nodes are at different distances from the source of thesounding pulse (that is, from the target). In that case, the nodes mayagree on a common start and stop time for the capture window, but theactual incoming signal will appear at different times within thatcapture window for each particular node, specific to the time of arrivalat the particular node. To time-reverse the signal, the elements re-emitthe time reversed capture window according to a pre-arranged protocol.There is no requirement to calculate the different delays of signalsgenerated by the sounding pulse and lying within the shared capturewindow. Also, there is no requirement to adjust the emission times ofeach array member as the signal is retrodirected. Each array member maysimply read back the time-reversed capture window, starting at the sametime. As in the capture process, it is the boundaries of the reversedcapture windows that become the identical time reference points, not thephysical signals contained inside the capture windows. The shared(common) window approach, however, presumes that each element has aclock that is fully synchronized with the clocks in the other arrayelements, so as to enable the elements to agree on the time boundariesof the window.

In embodiments, a system uses local oscillators to downconvert andupconvert the signals, and only the baseband or IF signals captured inthe digital sampling infrastructure are contained in the capture window,thereby reducing the accuracy of time synchronization required. Thephase components of the channel propagation paths may be contained inthe baseband signal and are managed by the TR process as describedabove, so the only residual alignment of phases that is required may beensuring that the phases of the local oscillators are equalized or phaseconjugated, as is described above. There is no requirement to align theLOs to compensate for the channel phase, because channel phase alignmentis provided by implementing a TR process with a capture window.

It is possible to operate arrays in a mode that is a hybrid of theabove-described configurations, depending on the applications. We havestated above that in retrodirective beamforming, only alignment of thecapture window boundaries need to be accomplished. A question arises howto ascertain that the time sync across the nodes has successfullyaligned the capture window boundaries to produce focusing at the target.It works in theory, but real-life systems may be prone to errors andfaults and reductions in the ability to measure time boundaries in lowSNR environments may be observed. One of the benefits of a closed loopsystem is that it can be verified that the process has been correctlyimplemented. A benefit of the techniques described in this document isthat once time-sync has been achieved, the techniques should work forall targets as long as the correct sounding pulse associated with agiven target is acquired. Thus, it may be possible to use a cooperativearray process to align the members of the array, for example,software-defined radios carried by soldiers in a patrol or squad. Oneelement of the array, which may be referred to as the master, may setitself up as a temporary target, i.e., configure the rest of the arrayto perform effective beamfocusing on the master as the controlledtarget. Since the master is actually one of the array nodes, it isreasonably assumed that it can interoperate cooperatively with the otherarray nodes. In embodiments, the master may also be the clock referencewhich will be shared between or among the nodes of the array. Inembodiments, the master can recognize and identify signals sent by anyother node of the array, for example, by the presence of a node-specificpilot embedded in the signal, or other techniques that are known tothose skilled in the art. In these embodiments, since the master is aunique node of the system, it may also be able to communicate in a morespecialized manner than an arbitrary target receiver and may be able toinstruct the other nodes to adjust their parameters until the masterdetermines that an optimal focus is achieved. For example, the mastermay be able to instruct only Node 1 of the array to adjust its phaseuntil the master observes the focused power maximized. It may theninstruct Node 2 of the array to adjust its phase, further enhancing thefocus, and so on through the rest of the nodes. This is an iterativeoptimization which can be done with a closed loop process, which processis available between the master and the other nodes of the array. Inembodiments, the nodes emit small amplitude sinusoidal pilot signalsembedded into the phase terms of the local oscillators. A smallcosinusoidal pilot tone of frequency ω_(pilot) appearing on a signalthat is described essentially by cos(φ+φ₀ cos(ω_(pilot)t)) should vanishas the signal approaches the maximum or the “peak” of the cosinusoidalsignal, i.e., where φ→0,2nπ. The master may be configured to instructthe nodes to adjust their phases/delays until it observes all thesignals correctly nulled in the focused spot.

To summarize this aspect, the array is configured so that the masternode of the array has the ability to set itself up as a proxy target,and then being able to recognize when an alignment process has beenimproved or even optimized. This allows the array to achieve correctclock synchronization, which can be verified when the array successfullyfocused on the master. In the process described above, clocksynchronization is a pre-requisite for any form of coherent focusing,and in the process described, clock synchronization can be performedindependent of any specific target. In other words, once thesynchronization process is achieved by focusing on the master, it doesnot need to be repeated for a different use of the array. The differentuse may then be beamfocusing on a remote target, which is not part ofthe array. The master may also participate in the beamfocusing on theremote target as one of the array nodes. In particular, if the masterwas the clock reference source during the time sync process, then bydefinition it can insert itself into the array as an array member forbeamforming purposes, and its correct alignment should be guaranteed.

Various imperfections in the alignment, for example, frequency offsetsof the carriers, may cause the synchronization to degrade, and requireit to be re-established periodically.

In the communication applications described above, the multi-elementarray generally operates according to a pre-agreed protocol that isfollowed by all the elements of the array. This is not surprising,because it is generally true for systems of networked nodes that arerequired to interoperate in a network.

FIG. 10 is a summary diagram of certain attributes of the open looparrays, retrodirective arrays, and cooperative arrays discussed above.

As we have already mentioned, one type of array of concern here is anarray of nodes that are untethered, possibly in motion relative to thetarget and/or each other, which may be at unknown locations, and withindividual LO references. We may refer to such arrays of emitters asDynamic Phased Arrays (DPA) or ad hoc arrays. Note that the “motion”here may include changes in coordinates, changes in orientation, andchanges in both coordinates and orientation. Important issues with sucharrays include the scalability of the arrays and the limits imposed onthem by their ad hoc (dynamic) nature. In particular, array size,distribution of array elements, accuracy of the clocks of the arrayelements, and motion of the elements may affect a variety of arrayperformance parameters, such as gain, bandwidth, latency, andbeamforming accuracy. Motion of the array nodes may also introduceDoppler shifts, which may under some conditions cause frequency offsets.

In selected embodiments in accordance with this description, abeamforming array utilizes a cooperative approach to produce phase,frequency and time alignment of the elements of the array fortransmission to a target receiver, and uses retrodirective arraytechniques with time-reversal to manage the main channel between thearray and the target receiver once the system has determined that thearray elements have achieved the requisite alignment properties. In someof these embodiments, the synchronization and beamforming are brokeninto two stages: (1) carrier phase/frequency alignment, and (2)modulation envelope and phase alignment. This alignment process does notrequire feedback from the intended receiver to align carriers of thedistributed nodes. A typical case where an array separates the carrieralignment process from the pulse envelope alignment process is when thesignal at the array is reduced to a baseband or IF frequency forprocessing purposes, by mixing with a Local Oscillators at the arraynodes. In describing such arrays in more detail and in analyzing certainconsiderations affecting such arrays, this document also examines howthe array alignment process as well as the main channel beamfocusingscale with array size, distance between the array members, and distanceto the target receiver (the distance between the opposite end of themain channel from the array).

Time, Frequency and Phase Synchronization.

Method of achieving the synchronization of the array. In the discussionof synchronization of the various elements (nodes, member) of the array,N refers the total number of the elements. One of the elements may bedesignated as the master, that is, the element of the array with somespecial function such as the responsibility for performing thesynchronization. The remaining (N−1) array elements (slaves) performrepeated back and forth communications with the master. Often, the arrayhas more than three elements, so (N−1) is equal to 2 or more. A distanced_(mean) is defined as the average distance of the slave members fromthe master. Note that d_(mean) is not the average distance between themembers, but the average distance to the Master. As will be seen below,the latency of the synchronization process depends, among other factors,on N and d_(mean).

In one example of an embodiment, a round robin algorithm is used: afirst slave performs a back and forth alignment process with the master;when the first slave has completed its alignment, another slave takesits turn, and so on until all the slaves sequentially set up thealignment. The latency of synchronization in round robin implementationsis dominated by the latency of this algorithm. The latency increaseswith distance and also in proportion to (N−1).

In an example of alignment process, first phase alignment is performed.For phase alignment, each slave node of the array sends a signal to themaster node of the array, which then captures and reflects the signal,thus enabling the slave node to calculate and correct the phase offsetrelative to the master node. At this point in time, there is no simpleway to determine how much of the phase offset resulted from theprocessing by the master and how much was due to an unknown propagationdelay between the two nodes (master node to slave node round trippropagation delay). What is more, at this point, the slave node cannotbe assumed to have a defined time reference to allow it to measure theround trip latency which enables it to resolve how much of the phaseshift resulted from the propagation delay. However, a second measurementcan be made which allows frequency alignment to be established, becausefrequency is the time derivative of phase. A second phase offset can bemeasured and the difference between this second phase offset measurementand the previous measurement gives the frequency offset, that is, thedifference in the phase offsets over the time between the two phasemeasurements. The slaves (at least one of the array elements) adjustphase and frequency until no time dependence of phase is observed,within certain predetermined bounds. When the phase offset no longerappears to vary between measurements, the nodes are operating atessentially the same frequency, at least over a time scale long comparedto the back and forth latency which even if not yet known precisely canstill be estimated. The system is now only limited by the intrinsiccoherence of the clocks.

Once common frequency has been established, a process to determine timesynchronization and phase alignment is performed.

Time Synchronization and Phase Alignment.

Frequency synchronization establishes a common clock rate. A timeinterval can now be determined by a protocol. In one embodiment, thisprotocol may instruct the nodes to define a predetermined time period(e.g., one msec) as a predetermined number (e.g., n) cycles of thecommon clock. Other embodiments are also feasible. This process can beimplemented for example by the Master emitting two pulses pre-defined tobe, for example one millisecond apart. Each Slave node then adjusts itsclock rate until n cycles, as defined by an agreed protocol, haveelapsed between the two received pulses. This allows the Slaves to reachan agreed time synchronization standard that defines a common clock rateand a common time unit standard that are defined by the Master andshared by the Slaves.

Once this shared time standard has been established the Slave nodes canestablish a common time standard that allows them, for example, tomeasure the time delay of a signal sent from the Salve to the Master andthen reflected back from the Master. By using the known speed ofpropagation of the signals, e.g., the speed of light, the Slave can thenalso infer distances.

After the frequencies are aligned in this manner and a time standard isshared, the Slaves can implement a process where they align the phasesof their local oscillators, which is important for the correct operationof the phased-array as described above. In one embodiment, the Slaveemit a signal with the phase of the signal linked to its LO phase asdescribed above. The Master then returns this signal to the Slave, whichcompares the phase of the returning signal to the continuously runningphase of the Slave's LO. In one embodiment, the Slaves perform thismeasurement sequentially, first Slave 1 then Slave 2, etc., enabling theMaster to correctly interface with each Slave in a unique manner. Sinceeach Slave now has a time reference, it can also measure the round triplatency and estimate how many cycles, i.e., phase offset of the LOshould have evolved during that time period. This number is thencompared to the actual measured phase offset and the difference can onlybe due to any additional phase offset added by the master when itreturned the signal emitted by the slave. This information now providesthe slave with a mechanism, which in one embodiment allows the slave toadjust its phase until the calculated residual phase offset is nulled.In another embodiment, phase offset is not nulled but the results arestored and used as corrections to be applied at each node when the arraysubsequently operates in time-reversal mode on the main channel (thatis, the channel between the array and the target). To summarize we havedescribed an implementation where the Master is set as a reference nodeand the Slaves first acquire frequency sync, then apply time sync basedon the frequency sync and then perform phase sync by removing phasesmeasured by accurate measurement of the propagation time with respect tosignals transmitted between the Slaves and the reference master node.

After each Slave has implemented this process (in a sequential manner orotherwise), each Slave becomes frequency, time, and phase synchronizedwith the Master. Other embodiments are possible.

As with all physical alignment processes, the system may experienceerrors and require an iterative correction process. For example,multiple iterations may be required to produce frequency synchronizationor time synchronization that is required to achieve a predeterminedlevel of accuracy or another performance measure.

We have now defined a time synchronization process that permits allnodes of the array to perform actions at the same times. A predefinedprotocol may be used to label any given time. For example, if all nodesare to perform an action at a specific time (such as launching asignal), the Master may establish the time synchronization, and canapply a time label to a signal. In order to establish correct time sync,the Slaves may correct the time label to allow for the known time delayto the Master, as described above. Once this process has been performed,the nodes can operate with a shared time reference. All descriptions sofar have described the time synchronization between the members of thearray. This permits the nodes of the array to operate synchronously as aphased array to capture and process signals from an external target.

In one embodiment, this allows the Master to instruct all Slaves tostart measuring the Capture Window at a time t=t0 and to finish at timet=t1. The above described alignment process should ensure that all thenodes will indeed be correctly synchronized.

In many conditions, the total phase alignment latency Δt across theentire array, can be shown to vary approximately as

${\left( {N - 1} \right)\frac{2d_{mean}}{c}},$where c is the speed of light, d_(mean) is the mean distance from thetarget to the array and

$\left( {\Delta\;{\left. t \right.\sim\left( {N - 1} \right)}\frac{2d_{mean}}{c}} \right).$Initially the frequency alignment may need multiple (e.g., 2, 3, 4, 5,possibly more) iterative repeats of this to reach sufficient accuracy;once the frequency has been aligned, however, subsequent single phasealignment steps may be adequate to perform an adjustment of thefrequency for typical Allan variances of a quartz clock. Typical updaterates may be 5 milliseconds or less, plus the latency (which my be

$\left. {{\Delta\; t} = {\left( {N - 1} \right)\frac{2d_{mean}}{c}}} \right).$

FIG. 11 shows graphs of alignment latency as a function of the meandistances scale, for 5, 10, 15, and 20 element arrays.

Clearly, as the array increases its scale (i.e., mean separation betweenthe Master and other array elements and/or the number of the arrayelements increase), the round trip latency required to synchronize thearray becomes the dominant factor. It may become greater than anycomputation time due to calculations which is typically in the 10s to100s of nanoseconds, except for small arrays with low mean separation.However, as the scale of the array continues to increase, at some pointa limit will be reached set by the clock coherence. In this extremecase, it may not be possible to align the system rapidly enough, beforethe clock coherence degraded so far as to require that the alignment berefreshed. However, even when the latencies are relatively small, it maybe necessary to repeat the synchronization since the timing sync iseventually lost due to random drift of the clock, rather thandeterministic misalignment due to fixed phase and frequency offsets.This is usually determined by the Allan variance of the clocks used;however, any implementation that performs a lot of division andmultiplication of clock frequencies and/or other computationallyexpensive operations may experience timing variances worse that theAllan variance of quartz or an atomic clock. In a particular embodiment,a repeat window of ˜5 milliseconds is used, which may be significantlyfaster (shorter duration) than what is required to stabilize for theAllan variance of quartz. The effective variance for the entire arraymay be determined by the effective clock coherence time of the entirearray.

If each clock in an N element array has a timing variance σ², then theeffective variance of the entire array is var=Nσ². Hence the effectivecoherence time of the entire array may be

${{\Delta\; t_{array}} = \frac{\Delta\; t_{coh}}{\sqrt{N}}},$where t_(coh) is the coherence time of the clocks of the array elements.This helps us understand why operating a dynamic, untethered distributedphased-array is such a challenging process compared to existingstate-of-the-art phased-arrays with a distributed high precision centralclock.

FIG. 11 shows that, for moderate arrays with even simple quartz clocks,the mean distance of the arrays can be as large as 10 km, which is muchlarger than what would be practically considered in most ground basedscenarios, e.g., a squad of soldiers on patrol in an urban environment,or even for airborne applications such as configuring a “flock” ofunmanned aerial vehicles (UAVs) to act as a phased array. This of coursedoes not preclude the use of other clocks, such as atomic clocks, inground based applications. Atomic clocks may also be more suitable forspace-based satellite applications, with their much larger distances andthe consequent longer latency of the alignment process.

In embodiments, array nodes are aligned into a distributed time reversalmirror for communication with a target. The nodes use a standard up/downconversion receivers and transmitters, meaning that the array canoperate with standard radio architectures using digital signalprocessing structures in the digital I/Q path of the radio where thesignals are processed at an intermediate frequency (IF) or at baseband.For convenience, here we will refer to both the IF frequency and thetrue baseband signal as “baseband,” to distinguish them from the carrierfrequency, but this use of the term does not indicate that the signal isnecessarily downconverted to DC (zero frequency); it may have a smallfrequency offset that can be captured by the A/D and D/Asamplers/converters. This downconversion is often done to avoid the needto have an A/D and D/A sampling infrastructure operating at the highcarrier frequency. It is generally much more economical to have thesampling performed at “baseband.” The time synchronization thus onlyneeds to be accurate enough to permit the system to operate at themaximum sampling rate, which is set by the Nyquist criterion at twotimes the maximum baseband frequency, or some increase over that rate toallow margin for error.

Various algorithms may be employed to separate the symbol time alignmentand the carrier phase alignment along with the spatial alignment(beamforming weights). An elegant reciprocity-based method is used tosynchronize distributed nodes and determine the optimal beamformingweights to collaboratively communicate to a target receiver. Thesynchronization and alignment are broken up into separate independentsteps, to relax alignment procedure and requirements of the LO Phase,Frequency, Time Offset, and spatial alignment. The array performs theclock alignment using a reciprocal architecture where one node (e.g.,slave TX1 of FIG. 3) sends out a signal to another node (e.g., masterTX2 of FIG. 3), and TX2 retrodirects that signal (or some processedversion of it) back to TX1.

FIG. 12 illustrates selected aspects of this approach using a standardupconversion-downconversion architecture, where only the differenceterms are kept by the receiver because of “baseband” architectureconstraints. The transmit data at baseband is first upconverted (theplus sign in the exponent next to the upconverter 1205) using TX1's LOto an RF frequency of ω_(i) with phase φ₁. The RF signal is passedthrough a channel 1210 and undergoes a time-of-flight (channellength/speed of light) dependent phase shift of φ_(c). The RF signalsent by TX1 is received by TX2 and then downconverted (the minus sign inthe exponent next to a downconverter 1215) using TX2's LO with a carrierRF frequency of ω₂ and phase φ₂. The TX2 node can then do basebandoperations or IF operations, in this case at IF frequency (ω₁−ω₂). Theseoperations are typically at low enough frequency so that they can beperformed in an FPGA/CPU. To send the signal back, TX2 upconverts thesignal (the plus sign in the exponent next to an upconverter 1220) usingits LO. For example, in the case shown the signal is reconverted to(ω₁−ω₂+ω₂)=ω₁. It then sends the signal back to TX1 through the channel1210 with an additional channel phase shift of φ_(c). The TX1 nodereceives this signal at its antenna and downconverts the signal tobaseband with its downconverter 1225. The up/down conversion processesintrinsically measure the phase (and frequency) offset of the incomingsignal relative to the phase and frequency of the LO used in the up/downconversion process. Hence, the system can intrinsically keep track ofphase and frequency errors between the signal and the local oscillatorsand can use this information to correct the phase and frequency. Itshould be noted that when these processes are applied between the arraymembers, time reversal is not used as it was used between the array andthe target. Here, the intent is to recover a signal that represents thephase difference between the array nodes so that the LO phases may becorrected, whereas the TR applied on the main channel is intended toeliminate the combined path and LO phase difference.

Techniques other than adjustment of a direct digital synthesizer may beused to compensate TX1's LO. For example, phased-locked loop (PLL)techniques may be used, where the measured phase/frequency differencesare used to retune the LO. But the direct digital synthesis (DDS)correction method may be more accurate, and may eliminate the need forspecial oscillator circuitry.

Phase correction of the carrier may be easier to achieve, because thecorrection is for relative phase offsets of two continuous wave (CW)signals. Since the signals are CW, phase offsets will be between 0° and360°, and wrap around with each period. That is, a 10° phase shift isequivalent to a 370° (360°+10°) phase shift. Absolute phase orpico-second time synchronization is not needed here, which maysignificantly relax measurement requirements.

Described above is the phase alignment process with two nodes (TX1/TX2),and the process may be scaled for N>2 number of nodes. The timealignment may be done in a round-robin fashion pair-wise between theMaster and each slave (each of the other nodes). In embodiments, largerarrays with 10 to 100 use this technique.

Frequency offsets can be derived from phase offset measurements bytaking the derivative of the phase between the alignments, such asdividing the difference between successive phase offset measurements bythe time between the measurements. If DDS is used, the DDS circuitry mayupdate a phase accumulator to track the reference frequency in bothphase and frequency. In selected embodiments, this method is limited toa frequency acquisition range proportional to limiting the phase changeto a maximum of a single cycle over the refresh interval. Thislimitation may be overcome by using a coarse frequency offset at systemstart-up and/or other times.

The second step of the synchronization process, time-alignment of dataat the modulation bandwidth, may be performed to within some fraction(e.g., 1/10 for within about −0.5 dB of ideal) of the modulationenvelope. This significantly relaxes the timing accuracy needed.

For 1 MSamp/sec, for example,

${\frac{1}{{BW}_{mod}} \times 10\%} = {100\mspace{14mu}{{ns}.}}$In embodiments designed to operate for node distance differences less100 ft, relative time alignment of the modulation envelope may beunnecessary, because the time-of-flight differences are small. Withlarger node distance differences, time alignment may be needed,particularly at the nanosecond time scale. This may be significantlyeasier than picosecond time alignment of other techniques.

FIG. 14 shows a process 1400 for communications from an array of nodesto a target. At flow point 1401, the nodes are powered up and ready tooperate.

In step 1405, phases of local clock references of all nodes of theplurality of radio frequency transmission nodes are aligned.

In step 1410, frequencies of the local clock references of all nodes ofthe plurality of radio frequency transmission nodes are aligned.

In step 1412, time references of all the nodes are aligned.

In step 1415, the data for transmission to the target is obtained ateach node.

In step 1420, the nodes receive a sounding signal from the target.

In step 1425, each node generates a time-reversed sounding signal atcarrier frequency, using (1) sample readout reversal at baseband, and(2) phase-conjugation at carrier frequency.

In step 1430, the nodes convolve the common data with the time-reversedsounding signal, to obtain transmission signal.

In step 1435, the nodes transmit the transmission signals so as to focuson the target in space and time.

At flow point 1499, the process may end, to be repeated in part or inwhole as needed.

The features described throughout this document may be presentindividually, or in any combination or permutation, except where thepresence or absence of specific elements/steps/limitations is inherentlyrequired, explicitly indicated, or otherwise made clear from thecontext.

Although the process steps and decisions (if decision blocks arepresent) may be described serially in this document, certain stepsand/or decisions may be performed by separate elements in conjunction orin parallel, asynchronously or synchronously, in a pipelined manner, orotherwise. There is no particular requirement that the steps anddecisions be performed in the same order in which this description liststhem or the Figures show them, except where a specific order isinherently required, explicitly indicated, or is otherwise made clearfrom the context. Furthermore, not every illustrated step and decisionblock may be required in every embodiment in accordance with theconcepts described in this document, while some steps and decisionblocks that have not been specifically illustrated may be desirable ornecessary in some embodiments in accordance with the concepts. It shouldbe noted, however, that specific embodiments/variants/examples use theparticular order(s) in which the steps and decisions (if applicable) areshown and/or described.

The instructions (machine executable code) corresponding to the methodsteps of the embodiments, variants, and examples disclosed in thisdocument may be embodied directly in hardware, in software, in firmware,or in combinations thereof. A software module may be stored in volatilememory, flash memory, Read Only Memory (ROM), Electrically ProgrammableROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), hard disk,a CD-ROM, a DVD-ROM, or other form of non-transitory storage mediumknown in the art. Exemplary storage medium or media may be coupled toone or more processors so that the one or more processors can readinformation from, and write information to, the storage medium or media.In an alternative, the storage medium or media may be integral to one ormore processors.

This document describes in detail the inventive apparatus, methods, andarticles of manufacture for communications and other techniques usingdistributed cooperating nodes. This was done for illustration purposesand, therefore, the foregoing description is not necessarily intended tolimit the spirit and scope of the invention(s) described. Neither thespecific embodiments of the invention(s) as a whole, nor those of theirfeatures necessarily limit the general principles underlying theinvention(s). The specific features described herein may be used in someembodiments, but not in others, without departure from the spirit andscope of the invention(s) as set forth herein. Various physicalarrangements of components and various step sequences also fall withinthe intended scope of the invention(s). Many additional modificationsare intended in the foregoing disclosure, and it will be appreciated bythose of ordinary skill in the pertinent art that in some instances somefeatures will be employed in the absence of a corresponding use of otherfeatures. The embodiments described above are illustrative and notnecessarily limiting, although they or their selected features may belimiting for some claims. The illustrative examples therefore do notnecessarily define the metes and bounds of the invention(s) and thelegal protection afforded the invention(s).

What is claimed is:
 1. A method of configuring a plurality of radiofrequency (RF) nodes into a distributed RF time reversal mirror fortransmitting to a target, the method comprising steps of: aligningphases of local clock references of all RF nodes of the plurality of RFnodes; aligning frequencies of the local clock references of all RFnodes of the plurality of RF nodes; and generating, by each RF node ofthe plurality of RF nodes, a time-reversed signal at carrier frequencyusing sample-reversal of a common time capture window of the pluralityof RF nodes at baseband and phase-conjugation of a sounding signal atthe carrier frequency, thereby obtaining a plurality of time-reversedsignals, a time-reversed signal of the plurality of time-reversedsignals per RF node of the plurality of RF nodes, the common timecapture window being common to the plurality of RF nodes.
 2. The methodof claim 1, wherein modulation envelopes of the time-reversed signals ofthe plurality of time-reversed signals are not aligned by the pluralityof RF nodes.
 3. The method of claim 1, wherein the step of aligningfrequencies comprises a plurality of phase alignments by at least someRF nodes of the plurality of RF nodes.
 4. The method of claim 1, whereina first RF node of the plurality of RF nodes is designated as Master andthe step of aligning phases is performed in a round-robin manner.
 5. Themethod of claim 1, further comprising: optimizing reception of time andspace focused emissions from multiple nodes of the plurality of nodes ata master node of the plurality of nodes.
 6. The method of claim 1,further comprising: receiving at said each RF node of the plurality ofRF nodes the sounding signal from the target within the common timecapture window.
 7. The method of claim 1, wherein the step of generatingcomprises I/Q processing.
 8. A method of operating a plurality of radiofrequency (RF) nodes as a distributed RF time reversal mirror fortransmission to a target, the method comprising steps of: aligningphases of local clock references of the plurality of RF nodes; aligningfrequencies of the local clock references of the plurality of RF nodes;aligning time references of the plurality of RF nodes; distributingcommon data to each RF node of the plurality of RF nodes; receiving asounding signal from the target within a common time capture window, bysaid each RF node of the plurality of RF nodes, the sounding signalbeing emitted or reflected by the target, the common time capture windowbeing common to the plurality of RF nodes; generating, at said each RFnode, a time-reversed sounding signal at carrier frequency, thetime-reversed sounding signal of said each RF node being generated bysample-reversal of the sounding signal received in the common timecapture window at baseband and by phase-conjugation at carrierfrequency; convolving, at said each RF node, the common data with thetime-reversed sounding signal of said each RF node, thereby obtaining atransmission signal of said each RF node; and transmitting, from saideach RF node, said transmission signal of said each RF node, wherein thestep of transmitting is performed at the same time from all the RF nodesof the plurality of RF nodes for coherent time-reverse focusing on thetarget in time and space.
 9. The method of claim 8, wherein the steps ofgenerating and convolving are performed using I/Q processing.
 10. Themethod of claim 9, wherein the step of aligning frequencies comprisesiterative measurements of node-to-node phase offsets.
 11. The method ofclaim 9, wherein the step of aligning time references comprises step fortime alignment of the plurality of RF nodes.
 12. The method of claim 9,wherein the plurality of RF nodes comprises a master node and at leasttwo slave nodes, the method further comprising: configuring theplurality of the RF nodes so that the master node serves as a proxytarget and the at least two slave nodes focus time-reversed mastersounding emissions on the master node in time and space; and attemptingto improve reception of the time-reversed master sounding emissions atthe master node; wherein the steps of configuring and attempting areperformed before the step of transmitting.
 13. A node comprising anantenna, a radio frequency transceiver coupled to the antenna, a localoscillator, and a processor coupled to the transceiver to controloperation of the transceiver, wherein the node belongs to a plurality ofnodes, the node comprising: means for phase alignment of the localoscillator with the local oscillators of other nodes of the plurality ofnodes; and means for frequency alignment of the local oscillator with ofthe local oscillators of the other nodes of the plurality of nodes;wherein the node is configured to receive a sounding signal from atarget within a time capture window common to the plurality of nodes;and generate a time-reversed sounding signal at carrier frequency usingsample-reversal of the time capture window at baseband andphase-conjugation of the sounding signal at carrier frequency.
 14. Thenode of claim 13, wherein the node is further configured to participatein attempting to improve reception of time and space focused emissionsfrom multiple nodes of the plurality of nodes at a master node of theplurality of nodes.
 15. The node as in claim 13, wherein the node isfurther configured to: receive common data for transmission by theplurality of nodes to the target; generate a transmission signal fromthe common data and the time-reversed sounding signal; and transmit thetransmission signal, wherein all the nodes of the plurality of nodestransmit simultaneously, resulting in coherent time-reverse focusing intime and space of transmissions carrying the common data from theplurality of nodes on the target.
 16. The node as in claim 15, whereinthe node is configured to generate the time-reversed sounding signal andthe transmission signal using I/Q processing.
 17. The node as in claim16, wherein the means for frequency alignment comprises means foriterative node-to-node phase offset measurements.
 18. The node as inclaim 16, further comprising means for time synchronization with atleast one other node of the plurality of nodes.
 19. An article ofmanufacture comprising non-volatile machine-readable storage medium withprogram code stored in the non-volatile machine-readable storage medium,the program code comprising instructions for configuring a plurality ofradio frequency (RF) nodes into a distributed RF time reversal mirrorfor transmitting to a target, the instructions comprising steps of:aligning phases of local clock references of all RF nodes of theplurality of RF nodes; aligning frequencies of the local clockreferences of all RF nodes of the plurality of RF nodes; and generatingby each RF node of the plurality of RF nodes a time-reversed signal atcarrier frequency using sample-reversal of a common time capture windowat baseband and phase-conjugation of a sounding signal at the carrierfrequency, thereby obtaining a plurality of time-reversed signals, atime-reversed signal of the plurality of time-reversed signals per RFnode of the plurality of RF nodes, the common time capture window beingcommon to the plurality of RF nodes.
 20. The article of manufacture ofclaim 19, wherein the instructions further comprise steps of: obtainingby said each RF node common data for transmission from the plurality ofRF nodes to the target; receiving by said each RF node the soundingsignal from the target within the common time capture window; convolvingby said each RF node the common data with the time-reversed soundingsignal generated by said each RF node, thereby obtaining a transmissionsignal corresponding to said each RF node; and transmitting by said eachRF node the transmission signal corresponding to said each RF node,wherein the step of transmitting is performed at the same time by allthe RF nodes of the plurality of RF nodes for coherent focusing on thetarget in time and space.